The complexity of human communication has often been taken as evidence that our language reflects a true evolutionary leap, bearing little resemblance to any other animal communication system. The putative uniqueness of the human language poses serious evolutionary and ethological challenges to a rational explanation of animal communication. In this talk I will review ethological, neuroanatomical, molecular and computational results from humans, marmosets and songbirds, to set boundaries for these challenges. Analytical tools from neuroscience, semiotics and graph theory will be employed to argue that human language shares many features with other animal communication systems, and that the most substantial difference lies in the enhanced human capacity for symbolic recursion. I will also show that structural features of speech can be used to quantitatively discriminate schizophrenic and manic subjects from non-psychotic subjects, or patients with Alzheimer’s disease from patients with mild cognitive impairment. The results indicate that the graph-theoretical analysis of vocalizations is key to the study of language-related deficits in humans, and may have great applicability in animal models. I will conclude by presenting a current experiment to probe the limits of marmoset vocal communication using real-time conditioning of spontaneous calls. The experiment has potential to shed light on core mechanisms underlying language, and to serve as a naturalistic behavioral setting for the investigation of language disorders. Uncovering the processes that generate vocal communication in primates may prove crucial to our understanding of the origin of human language.